Respuesta :
Answer:
a)
[tex]\frac{1}{2048}[/tex]b)
[tex]\frac{1}{2048}[/tex]Explanation:
a) Given:
Flipping eleven fair coins
To find:
The theoretical probability that all eleven will come up tails
Recall the below probability formula;
[tex]Probability=\frac{Number\text{ of favourable outcomes}}{Total\text{ number of possible outcomes}}[/tex]If one fair coin is flipped, the total number of possible outcomes is 2 (HT) and the probability of obtaining a tail will 1/2.
So if eleven coins are flipped, the probability that all eleven will come up tails will be;
[tex]P(all\text{ }eleven\text{ }will\text{ }come\text{ }up\text{ }tails)=(\frac{1}{2})^{11}=\frac{1^{11}}{2^{11}}=\frac{1}{2048}[/tex]So the probability that all eleven will come up tails is 1/2048
b) The probability that the first toss is head is;
[tex]P(first\text{ toss is head\rparen }=\frac{1}{2}[/tex]The probability that the next ten are tails will be;
[tex]P(the\text{ }next\text{ }ten\text{ }are\text{ }tails)=(\frac{1}{2})^{10}=\frac{1^{10}}{2^{10}}=\frac{1}{1024}[/tex]Therefore the probability that the first toss is head AND the next ten are tails will be;
[tex]P(first\text{ }toss\text{ }is\text{ }head\text{ }AND\text{ }next\text{ }ten\text{ }are\text{ }tails)=\frac{1}{2}*\frac{1}{1024}=\frac{1}{2048}[/tex]So the probability that the first toss is head AND the next ten are tails is 1/2048
